the spinel structure

The spinel structure, named after the gemstone spinel (magnesium aluminate, MgAl2O4), is how ceramics accommodate two kinds of cation of different charge in one crystal, the AB2O4 formula. It is the host of the ferrites, the ceramic magnets in transformers, antennas and old-fashioned computer memory.

The oxygens form a face-centred-cubic close-packed array, and the cations fill some of the holes: one-eighth of the tetrahedral holes and one-half of the octahedral holes. The unit cell is large, holding eight formula units, so 32 oxygens, 8 cations in tetrahedral sites and 16 in octahedral sites. In a normal spinel like MgAl2O4 the 2+ A cations take the tetrahedral sites and the 3+ B cations take the octahedral ones; in an inverse spinel the arrangement is reshuffled, with the B cations split between both site types, magnetite (Fe3O4) is the classic inverse spinel.

This normal-versus-inverse choice is not a detail, it decides the material's magnetism. In the ferrites (MFe2O4, with M being Mn, Ni, Zn, Co) the way the cations distribute over tetrahedral and octahedral sites sets how their magnetic moments add up or cancel, and hence whether the ceramic makes a good soft magnet. Honest caveat: many real spinels are neither perfectly normal nor perfectly inverse but somewhere in between, and the degree of inversion shifts with temperature and processing, so the cation distribution, not just the formula, is what you must know to predict properties.